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# Why are 2 and 3 consecutive prime numbers?

Wiki User

2011-03-19 20:06:07

A Prime number is a number only divisible by 1 and itself, since nothing else goes into 2 but 1 and 2 and nothing goes into 3 but 1 and 3 they are both prime and since 3 goes after 2 they are consecutive

And they are the ONLY consecutive prime numbers because if you have one prime number (i.e. 29), then there always is an even number right after the prime number (i.e. 30 comes right after 29), and consecutive means "right next to," right? And we all know that even numbers can always be divided in half, so 2 and 3 are the only consecutive prime numbers.
1 is not a prime so that (1,2) is not a pair of consecutive integers that are prime. So, if there is another opair of consecutive numbers that are prime, they must be larger than (2,3) - ie the smaller of the pair must be greater than 2.

Now any pair of consecutive numbers must have one odd and one even number. Therefore, the candidate pair must contain an even number which is greater than 2. But all even numbers greater than 2 are divisible by 2 and so are composite (non-prime). So every such candidate pair contains an odd number which may or may not be prime, and an even number which is definitely not a prime.

Wiki User

2011-03-19 20:06:07
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